The British company that built the Shard skyscraper in London will manage the construction of the Kingdom tower in Saudi Arabia, which will be the world's tallest building when completed.

Mace, which also played a part in building the London Eye and renovating Oxford's Ashmolean Museum, has been appointed by the Jeddah Economic Company (JEC) to jointly oversee the £780m project with EC Harris, a British-based construction consultancy.

Exactly how far the Kingdom tower will rise above the sands of the Arabian desert near Jeddah is still a closely guarded secret, but JEC said it will be taller than the 830 metre Burj Khalifa, currently the world's tallest building. The company also said it would be four times as high as the 310 metre Shard, meaning it could top out at about 1,200 metres.

The Saudi Binladin group will begin construction later this year and the project should be completed in winter 2018.

The Saudi billionaire Prince Alwaleed bin Talal unveiled the plans, by American firm Adrian Smith + Gordon Gill Architecture, 18 months ago as part of a new £13bn Kingdom City development on the Red Sea coast to the north of Jeddah.

Tall buildings Photograph: Graphic

The chief executive of JEC, Waleed Abdul Jaleel Batterjee, said: "The vision of constructing the tallest tower in the world in Jeddah belongs to HRH Prince Alwaleed bin Talal. His vision is also that the project itself will set the world's sights on our beloved Kingdom of Saudi Arabia. Furthermore, the project will help create hundreds of jobs for our Saudi countrymen."

He told Building magazine that Mace was chosen because it was "going to use the same team that was on the Shard".

With a total construction area of more than 500,000 sq m, the Kingdom tower will include a five-star hotel, luxury flats, office space and the world's highest observatory, with breathtaking views of the Red Sea and the al-Sawarat mountains to the east.

Oil-rich Saudi Arabia has growing housing demands and is planning to spend about £260bn on infrastructure projects to meet its needs over the next five years.

Jeddah is the country's second largest city, with a population of 4 million. It has long complained of being neglected in favour of the capital, Riyadh, and recently had its bid to turn the old city into a Unesco world heritage site turned down.

Mark Reynolds, chief executive of Mace, said: "Kingdom tower is a project of international importance and immense ambition and we are delighted to be part of the team tasked with its delivery. As the client's project manager, I am confident we will deliver a development exemplary in innovation and approach."